The lowest drain in the house, if you have a basement, is generally the basement floor drain. Like all drains, the basement floor drain works using the power of gravity.
Basement floor drains are installed before the basement floor is poured, with a P-trap and a gentle horizontal outlet pipe tying into the main sewage outlet. The P-trap is that bump in the pipe you see under your sinks. It holds a reservoir of water near the opening of the drain that blocks bad smells from coming from the sewer back into the basement.
The drain will only work if the concrete for the basement floor is sloped to feed all floor water into it. It is fitted with a floor trap, but particulate matter can still infiltrate through the small holes of the trap. Traps are removable to provide access to clear blockages.
The basement floor drain is generally connected to the drainage system of the rest of the house, so when it clogs up, you have to figure out where the problem is. To do that, have someone flush the toilet upstairs, while you watch the drain aperture. If water rises in the aperture, the basement drain is not the problem. If not, there is a good chance your drain is not working because of an obstruction in the P-trap.